A Finite Element Formulation of Baraff-Witkin Cloth
Proceedings of Symposium on Computer Animation (SCA) 2020

Theodore Kim
Yale University
Department of Computer Science

Left: Stretched cloth using our FEM formulation. Right: Same cloth using original Baraff-Witkin formulas. Yes, I realize they look like face masks.


The Baraff-Witkin model has been a popular formulation for cloth for 20 years. However, its relationship to the finite element method (FEM) has always been unclear, because the model resists being written as an isotropic, hyperelastic strain energy. In this paper, we show that this is because the Baraff-Witkin model is actually a coupled anisotropic strain energy. We show that its stretching term approximates the isotropic As-Rigid-As-Possible (ARAP) energy, and its shearing term is a cross-fiber coupling energy common in biomechanics. While it has been known empirically for some time that the model can produce indefinite force Jacobians, the conditions under which they occur has never been clear. Our formulation enables a complete eigenanalysis that precisely characterizes exactly when indefiniteness occurs, and leads to fast, analytic, semi-positive-definite projection methods. Finally, our analysis suggests a generalized Baraff-Witkin energy with non-orthogonal warp and weft directions.

    Paper [PDF, 7.4 MB]
    Video [MOV, 64 MB]
     (Scroll down for YouTube)

    With Baraff-Witkin Stretching
With ARAP Stretching
Hammock / Face Mask
    With Original Baraff-Witkin Stretching
With FEM Baraff-Witkin Stretching
With St. Venant-Kirchhoff Stretching
With anisotropic stretching, v = [1 1]
With anisotropic stretching, v = [3 1]
    With Baraff-Witkin Stretching
With ARAP Stretching